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Combinatorics of Permutations, 2nd Edition
book

Combinatorics of Permutations, 2nd Edition

by Miklos Bona
April 2016
Intermediate to advanced content levelIntermediate to advanced
478 pages
14h 44m
English
Chapman and Hall/CRC
Content preview from Combinatorics of Permutations, 2nd Edition
3
In Many Circ les. Permutations as Products
of Cycles.
3.1 Decomposing a Permutation into Cycles
So far we have looked at permutations as linear orders, that is, ways of listing
n objects so that each object gets listed exactly once. In this section we will
discuss permutations from a different viewpoint. We will consider them as
functions. Let us redefine permutations along these lines.
DEFINITION 3.1 Let f :[n] [n] be a bijection. Then we say that f
is a permutation of the set [n].
This definition certainly does not contradict our former definition of permu-
tations. Formerly, we said that 34152 was a permutation of length five. Now
we can reformulate
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Publisher Resources

ISBN: 9781439850527